Praise be to Allah, and peace and blessings be upon the Messenger of Allah and his family.
In order to purify the impurity of urine, it is sufficient to pour water on the place where the impurity is, and the water should be of a greater amount than the impurity, so that it will disappear and no trace of it will be left. You do not have to wring out the garment after pouring water on it, because the remaining water is pure, so long as the impurity has disappeared.
An-Nawawi (may Allah have mercy on him) said in Rawdat at-Talibin, which is a book of Shafa`i jurisprudence (1/28): It is not stipulated in order to purify the garment that it should be wrung out, according to the more correct view. End quote.
It says in Mawahib al-Jalil Sharh Mukhtasar Khalil, which is a book of Maliki jurisprudence (1/250-251): He does not have to wring it out.
Commentary: That is, if the site of the impurity is washed with pure water, then the water leaves that place as pure water that has no trace of impurity, there is no need to wring the garment, because of the general meaning of the hadiths, and because the assumption is that the water that has left that spot is still pure, and the water that remains is the same as the water that is gone. End quote.
One of the texts which indicate that purification of garments and similar things from urine is achieved by pouring water greater in quantity than the impurity is the hadith of Anas ibn Malik (may Allah be pleased with him), according to which a Bedouin urinated in the mosque, and the people got up to deal with him, but the Messenger of Allah (blessings and peace of Allah be upon him) said: “Do not disturb him.” Then he called for a bucket of water and poured it over it. Narrated by al-Bukhari, 6205; Muslim, 284.
Al-Qadi `Iyyad (may Allah have mercy on him) said:
This hadith indicates that it is not stipulated, when washing impurities, that they should be scratched, and that it is sufficient, with regard to impurities that are in liquid form and are not viscous, to pour water over them only, and make sure that it reaches all of the impurity. This is in contrast to if the impurity is dried up or is viscous…
(End quote from Akmal al-Mu`allim, 2/110).
Al-Hafiz Ibn Hajar (may Allah have mercy on him) said:
This hadith is also quoted as evidence that it is not stipulated to wring out the water, because if that were stipulated, then the ground would not be pure until it dries, and the same applies to wringing out a garment, because there is no difference between (the ground and the garment).
End quote from Fat-h al-Bari, 1/325.
Based on that, both ways that you mention in the question are sufficient for the purpose of purification, because the impurity is a very small amount – one or two drops – and the water that you pour over it as you describe is usually sufficient to remove this impurity, so that no trace will be left of it.
Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said:
The most correct view is that when impurity has been removed by any means, the place is no longer to be deemed impure, for if the ruling is based on a reason, it ceases to apply when that reason is gone.
(End quote from Majmu` al-Fatawa, 21/475)
And Allah knows best.
